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Full Description
This is the second of three volumes that form the Encyclopedia of Special Functions, an extensive update of the Bateman Manuscript Project. Volume 2 covers multivariable special functions. When the Bateman project appeared, study of these was in an early stage, but revolutionary developments began to be made in the 1980s and have continued ever since. World-renowned experts survey these over the course of 12 chapters, each containing an extensive bibliography. The reader encounters different perspectives on a wide range of topics, from Dunkl theory, to Macdonald theory, to the various deep generalizations of classical hypergeometric functions to the several variables case, including the elliptic level. Particular attention is paid to the close relation of the subject with Lie theory, geometry, mathematical physics and combinatorics.
Contents
1. General overview of multivariable special functions Tom H. Koornwinder and Jasper V. Stokman; 2. Orthogonal polynomials of several variables Yuan Xu; 3. Appell and Lauricella hypergeometric functions Keiji Matsumoto; 4. A-Hypergeometric functions Nobuki Takayama; 5. Hypergeometric and basic hypergeometric series and integrals associated with root systems Michael J. Schlosser; 6. Elliptic hypergeometric functions associated with root systems Hjalmar Rosengren and S. Ole Warnaar; 7. Dunkl operators and related special functions Charles F. Dunkl; 8. Jacobi polynomials and hypergeometric functions associated with root systems Gert J. Heckman and Eric M. Opdam; 9. Macdonald-Koornwinder polynomials Jasper V. Stokman; 10. Combinatorial aspects of Macdonald and related polynomials Jim Haglund; 11. Knizhnik-Zamolodchikov type equations, Selberg integrals, and related special functions Vitaly Tarasov and Alexander Varchenko; 12. 9j-Coefficients and higher Joris Van der Jeugt; Index.
